To any positive contraction Q on `2(W ), there is associated a determinantal probability measure PQ on 2W , where W is a denumerable set. Let 0 be a countable sofic finitely generated group and G = (0, E) be a Cayley graph of 0. We show that if Q1 and Q2 are two 0-equivariant positive contractions on `2(0) or on `2(E) with Q1 ≤ Q2, then there exists a 0-invariant monotone coupling of the corres...

Abért and Weiss have shown that the Bernoulli shift s0 of a countably infinite group 0 is weakly contained in any free measure preserving action a of 0. Proving a conjecture of Ioana, we establish a strong version of this result by showing that s0 × a is weakly equivalent to a. Using random Bernoulli shifts introduced by Abért, Glasner, and Virag, we generalize this to non-free actions, replaci...

Let M be a connected 1-manifold, and let G be a finitely-generated nilpotent group of homeomorphisms of M . Our main result is that one can find a collection {Ii, j , Mi, j } of open disjoint intervals with dense union in M , such that the intervals are permuted by the action of G, and the restriction of the action to any Ii, j is trivial, while the restriction of the action to any Mi, j is min...

The theme of this issue of Artiicial Life is that traditional Dynamical Systems theory is inadequate for many problems in the study of Complex Systems. In this paper, I argue that the nite dimensional nature of traditional dynamical systems is inappropriate for evolutionary systems, but that simply embedding the dynamics into an innnite dimensional space overly complicates the mathematics and o...

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...